Multiple frequency method for nuclear magnetic resonance longitudinal relaxation measurement and pulsing sequence for power use optimization

ABSTRACT

A method for determining nuclear magnetic resonance longitudinal relaxation time of a medium. The method includes magnetically polarizing nuclei in the medium along a static magnetic field, momentarily inverting the magnetic polarization of the nuclei within each one of a plurality of different spatial volumes within the medium, transversely magnetizing the nuclei in each one of the spatial volumes after an individual recovery time corresponding to each one of the spatial volumes, and measuring an amplitude of a magnetic resonance signal from each one of the spatial volumes.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The invention is related to the field of nuclear magneticresonance (“NMR”) sensing apparatus, methods and measuring techniques.More specifically, the invention is related to NMR well loggingapparatus and methods for NMR sensing within earth formationssurrounding a wellbore. The invention also relates to methods for usingNMR measurements to determine petrophysical properties of the earthformations surrounding the wellbore.

[0003] 2. Description of the Related Art

[0004] The description of the background of this invention, and thedescription of the invention itself are approached in the context ofwell logging because well logging is a well known application of NMRmeasurement techniques. It is to be explicitly understood that theinvention is not limited to the field of well logging.

[0005] An apparatus described in U.S. Pat. No. 4,710,713 issued toTaicher et al is typical of NMR instruments used to measure certainpetrophysical properties of earth formations from within a wellboredrilled through the earth formations. NMR well logging instruments suchas the one disclosed by Taicher et al typically include a magnet forpolarizing nuclei in the earth formations surrounding the wellbore alonga static magnetic field, and at least one antenna for transmitting radiofrequency (“RF”) energy pulses into the formations. The RF pulsesreorient the spin axes of certain nuclei in the earth formations in apredetermined direction. As the spin axes precessionally rotate andreorient themselves into alignment with the static magnetic field, theyemit RF energy which can be detected by the antenna. The magnitude ofthe RF energy emitted by the precessing nuclei, and the rate at whichthe magnitude changes, are related to certain petrophysical propertiesof interest in the earth formations.

[0006] There are several principal operating parameters in NMR welllogging which should be optimized for efficient operation of an NMR welllogging instrument. These parameters include the logging speed (speed ofmotion of the instrument along the wellbore), the average and the peakpower supplied to the instrument and transmitted as RF pulses, and thesignal-to-noise ratio (“SNR”). Other parameters of interest include thevertical resolution of the instrument and the radial depth ofinvestigation of the measurements made by the instrument within theformations surrounding the wellbore. The last two of these parametersare primarily determined by the antenna and magnet configurations of theNMR logging instrument. Improvements to these two parameters are thesubject of numerous patents and other publications. Providing moreflexibility in the instrument's peak power requirements, and Limitationson the logging speed necessitated by the physics of NMR measurement havebeen more difficult to overcome.

[0007] A property of NMR measurements made in porous media such as earthformations is that there is typically a significant difference betweenthe longitudinal relaxation time (“T₁”) distribution and the transverserelaxation time (“T₂”) distribution of fluids filling the pore spaces ofthe porous medium. For example, light hydrocarbons and natural gas, ascommonly are present in the pore spaces of some earth formations, mayhave T₁ relaxation times as long as several seconds, while the T₂relaxation times may be only about {fraction (1/1000)} that amount. Thisaspect of NMR well logging is due primarily to the effect of diffusionoccurring within static magnetic field amplitude gradients. Theseamplitude gradients are mainly internal to the pore spaces of the earthformations, and are caused by differences in magnetic susceptibilitybetween the solid portion of the earth formation (referred to as therock “matrix”) and the fluid filling the pore spaces.

[0008] In order to perform precise NMR measurements on any medium,including earth formations, the nuclei of the material should bepolarized by the static magnetic field for about 5 times the longest T₁relaxation time of any individual component within the material. This isgenerally not the case for well logging NMR measurements, since someformation components, as previously explained, may have T₁ relaxationtimes as long as several seconds (requiring a polarization time of aslong as about 30 seconds). This is such a long polarization time as tomake impracticable having enough polarization time at commerciallyacceptable logging speeds. As the instrument moves along the wellbore,the earth formations which are subject to the static magnetic fieldinduced by the instrument are constantly changing. See for example, AnExperimental Investigation of Methane in Rock Materials, C. Straley,SPWLA Logging Symposium Transactions, paper AA (1997).

[0009] As a result of logging speed considerations, a polarization timeof 8 to 10 seconds has become more common for many NMR well loggingprocedures, including those used for natural gas detection. See forexample, Selection of Optimal Acquisition Parameters for MRIL Logs, R.Akkurt et al, The Log Analyst, Vol. 36, No. 6, pp. 43-52 (1996).

[0010] Typical NMR well logging measurement procedures includetransmission of a series of RF energy pulses in aCarr-Purcell-Meiboom-Gill (“CPMG”) pulse sequence. For well logginginstruments known in the art, the CPMG pulse sequences are about 0.5 to1 seconds in total duration, depending on the number of individualpulses and the time span (“TE”) between the individual RF pulses. Eachseries of CPMG pulses can be referred to as a “measurement set”.

[0011] In the typical NMR well logging procedure only about 5 to 10percent of the total amount of time in between each NMR measurement setis used for RF power transmission of the CPMG pulse sequence. Theremaining 90 to 95 percent of the time is used for polarizing the earthformations along the static magnetic field. Further, more than half ofthe total amount of time within any of the CPMG sequences actually takesplace between individual RF pulses, rather than during actualtransmission of RF power. As a result of the small fractional amount ofRF transmission time in the typical NMR measurement sequence, the RFpower transmitting components in the well logging instrument are usedinefficiently on a time basis. In well logging applications thisinefficiency can be detrimental to the overall ability to obtainaccurate NMR measurements, because the amount of electrical power whichcan reasonably be supplied to the NMR logging instrument (some of which,of course, is used to generate the RF pulses for the NMR measurements)is limited by the power carrying capability of an electrical cable whichis used to move the logging instrument through the wellbore.

[0012] Several methods are known in the art for dealing with the problemof non-transmitting time in an NMR measurement set. The first methodassumes a known, fixed relationship between T₁ and T₂, as suggested forexample, in Processing of Data from an NMR Logging Tool, R. Freedman etal, Society of Petroleum Engineers paper no. 30560 (1995). Based on theassumption of a fixed relationship between T₁ and T₂, the waiting(repolarization) time between individual CPMG measurement sequences isshortened and the measurement results are adjusted using the values ofT₂ measured during the CPMG sequences. Disadvantages of this method aredescribed, for example in, Selection of Optimal Acquisition Parametersfor MRIL Logs, R. Akkurt et al, The Log Analyst, vol. 36, no. 6. pp.43-52 (1996). These disadvantages can be summarized as follows. First,the relationship between T₁ and T₂ is not a fixed one, and in fact canvary over a wide range, making any adjustment to the purported T₁measurement based on the T₂ measurements inaccurate at best. Second, inporous media T₁ and T₂ are distributions rather than single values. Ithas proven difficult to “adjust” T₁ distributions based on distributionsof T₂ values.

[0013] Another method known in the art for increasing the powerefficiency of an NMR well logging instrument is described, for examplein, Improved Log Quality with a Dual-Frequency Pulsed NMR Tool, R. N.Chandler et al, Society of Petroleum Engineers paper no. 28365 (1994).The Chandler et al reference describes using large downhole capacitorsto store electrical energy during the waiting (repolarization) time andthen using high peak-power during application of the RF pulses in theCPMG sequences to improve the signal-to-noise ratio (“SNR”). There areseveral disadvantages to the method described in the Chandler et alreference. First, it is very expensive to have large capacitors in awell logging instrument, which must be able to operate at hightemperature (generally in excess of 350° F.). Second, using high peak RFpower to improve SNR involves complicated and expensive transmitterswitching circuits. The switching circuit design problem is only madeworse by the requirement that the well logging instrument be able towithstand 350° F. or more. Using high peak power is also not veryeffective for the purpose of improving SNR because the SNR increasesonly as the fourth root of the increase in the peak RF pulse power.

[0014] Another NMR logging apparatus, known as the Combinable MagneticResonance (“CMR”) logging tool, is described in U.S. Pat. No. 5,432,446issued to MacInnis et al. The CMR logging tool includes permanentmagnets arranged to induce a magnetic field at two different lateraldistances along the wellbore and at two different radial depths ofinvestigation within the earth formation. Each depth of investigationhas substantially zero magnetic field amplitude gradient within apredetermined sensitive volume. The objective of apparatus disclosed inthe MacInnis et al '446 patent is to compare the output indications fromthe first and the second sensitive volumes to determine the effects ofborehole fluid “invasion” on the NMR measurements. A drawback to the CMRtool, however, is that both its sensitive volumes are only about 0.8 cmaway from the tool surface and extend only to about 2.5 cm radiallyoutward from the tool surface into the earth formation. Measurementsmade by the CMR tool are subject to large error caused by, among otherthings, roughness in the wall of the wellbore, by deposits of the solidphase of the drilling mud (called “mudcake”) onto the wall of thewellbore in any substantial thickness, and by the fluid content of theformation in the invaded zone.

[0015] In NMR well logging measuring techniques, reducing the so-called“dead time” (the time between an initial 90 degree RF pulse and a firstone of the 180 degree rephasing pulses in the CPMG sequence) duringwhich no spin-echo measurements are made due to “ringing” of the antennain the static magnetic field) is important in order to be able toresolve the presence of earth formation components having very short T₂times. As the dead time is reduced, it becomes necessary in a CPMG pulsesequence to reduce the amount of time (“TE”) between individual 180degree rephasing pulses in the CPMG sequence. Some devices, such as onedescribed in, Measurement of Total NMR Porosity Adds New Value to NMRLogging, R. Freedman et al. SPWLA Logging Symposium Transactions, paperOO (1997), have achieved a time-to-first-echo (and subsequent TE) of asshort as 0.2 milliseconds (msec). Since the expected T₂ distribution oftypical earth formations extends to one second or more, however, a CPMGmeasurement sequence of at least 1 sec total length is required tomeasure the petrophysical properties of typical earth formations. Theresult of the combination of the need to measure very short and verylong T₂ relaxation time components results in an CPMG measurementsequence including 8,000 or more echoes (“echo train”) using instrumentssuch as the CMR.

[0016] Most petrophysical parameters of interest such as irreduciblewater saturation, fractional volume of movable (“free”) fluid,permeability, etc. are based on only one differentiation between “short”(defined as between 0 and about 33 msec) and “long” (defined as morethan about 33 msec) parts of the T₂ distribution. Assuming the CPMGpulse sequence (and resulting “echo train”) is about 1 sec in duration,only about 3 percent of the total duration of the echo train issubstantially sensitive to components of the earth formation havingshort T₂ values, as compared to about 97 percent of the echo train beingsubstantially sensitive to components of the earth formation having longT₂ values. The nature of the typical echo train therefore results instable, precise values for parameters such as the fractional volume offree fluid (“FFI”), but can result in unsatisfactory stability andprecision in the values determined for other petrophysical propertiessuch as the irreducible water saturation (“BVI”). See for example,Improved Log Quality with a Dual-Frequency Pulsed NMR Tool, R. N.Chandler et al, Society of Petroleum Engineers paper no. 28365 (1994).

[0017] Because the nature of the relationship between petrophysicalproperties of interest and certain NMR properties is at best uncertain,it is desirable to be able to measure the longitudinal relaxation timeT₁ of the earth formations. In NMR well logging measuring techniques,however, T₁ measurement has not proven to be practical using the NMRlogging apparatus and techniques known in the art. Even if only lowaccuracy were required, the most the efficient methods of measuring T₁would require at least several seconds in between individual measurementsets to enable the nuclei in the earth formations to repolarize alongthe static magnetic field. Historically, most laboratory and all fieldmeasurements of the petrophysical properties of earth formations werelimited to measurements of T₁. Based on these results, relationshipsbetween the petrophysical properties and the relaxation time T₁ wereestablished. As a matter of practical necessity, however, mostcommercial applications of NMR measurement to well logging substitutethe T₁ relaxation time by measurements of the T₂ relaxation time. Inmost cases, however, the direct substitution of T₁ by T₂ forpetrophysical interpretation cannot be substantiated. The principalreason for the lack of direct ability to substitute T₁ for T₂, is thatT₂ is often affected by molecular diffusion within the internal magneticfield gradients present in the pore spaces of earth formations. Theseinternal gradients are caused by differences in magnetic susceptibility,in the presence of the static magnetic field imparted by the NMRinstrument, between the solid portion of the earth formations (the rock“matrix”) and the fluid in the pore spaces. Smaller size pore spacesgenerally have larger internal magnetic field gradients than do largerpore spaces, therefore any correlation between pore size and T₁distribution cannot be directly related to a correlation between poresize and T₂ distribution.

[0018] A method for increasing the time efficiency of NMR pulsingsequences is described in U.S. Pat. No. 4,832,037 issued to Granot. Themethod described in the Granot '037 patent includes applying a staticmagnetic field to materials to be analyzed, momentarily applying agradient field to the materials to be analyzed, and applying an RF pulseto an antenna at a first frequency to transversely polarize the nucleiof the material within a specific geometric region. The specificgeometric region is the location at which the total magnetic fieldstrength, which is the sum of the static field and the gradient field,corresponds to the Larmor frequency of the polarized nuclei within thespecific geometric region. After the gradient field is switched off, thefree induction decay (“FID”) signal is measured and spectrally analyzed.During a waiting time, generally about equal to T₁, between successivemagnetic resonance experiments in the same specific geometric region,additional gradient pulses and RF pulses at different frequencies can beapplied to measure the FID signal from different geometric regionswithin the materials to be analyzed. By measuring the FID signal fromwithin different geometric regions during the waiting time, a pluralityof different regions in the materials can be analyzed substantially inthe same time span as needed to analyze a single geometric region withinthe materials. The method in the Granot '037 patent is not useful forwell logging, however. First, using gradient pulses as needed for theGranot technique would dramatically increase the power consumption ofthe well logging instrument. Since the power carrying capacity of thewell logging cable is limited, it is not preferred to have additionaluses of power in the well logging instrument such as energizing gradientcoils. Second, the method in the Granot '037 patent is intendedprimarily for measurements of the FID signal, rather than measurementsof spin echo amplitude decay and T₂ as is more typical of well loggingtechniques. Using momentary gradient fields superimposed on the staticmagnetic field would make it difficult to measure spin echo amplitudedecay and T₂ since the polarized nuclei in earth formations in anyspatial volume would not have an opportunity to return to magneticequilibrium between successive measurements made according to thetechnique disclosed in the Granot '037 patent.

SUMMARY OF THE INVENTION

[0019] The invention is a method for determining the nuclear magneticresonance longitudinal relaxation time (T₁) of a medium. The methodincludes magnetically polarizing nuclei in the medium along a staticmagnetic field. The nuclei are momentarily inverted as to their magneticpolarization within each one of a plurality of different spatial volumeswithin the medium. The inversion is performed by transmitting a seriesof 180° pulses each at a frequency corresponding to the static magneticfield strength within each sensitive volume. The nuclei in eachsensitive volume are then transversely magnetized after an individualrecovery time corresponding to each one of the spatial volumes. Anamplitude of a magnetic resonance signal from each one of ,he spatialvolumes is measured in order to calculate the T₁ relaxation curve. Inthe preferred embodiment of the invention, the transverse magnetizationis induced in each one of the individual sensitive volumes bytransmitting radio frequency pulses at frequencies corresponding to thestatic magnetic field strength within each sensitive volume. In thepreferred embodiment, the transverse magnetization is performed bytransmitting a series of CPMG “read-out” pulse sequences, each sequencetransmitted at a frequency corresponding to each one of the sensitivevolumes, and including measuring the amplitude of the resulting spinechoes in each CPMG sequence.

[0020] In another aspect of the invention, the transverse relaxationtime distribution of the medium can he measured with an improvedsignal-to-noise ratio. The medium is polarized along a static magneticfield. A first CPMG echo train is acquired from within a first sensitivevolume. The first CPMG train has an inter-echo spacing and a durationlarge enough to determine the presence of slowly relaxing components inthe medium. Then a plurality of additional CPMG echo trains is acquired.Each of the additional echo trains corresponds to a different sensitivevolume, and each of the additional CPMG echo trains has an inter-echospacing and a duration less than the duration and echo spacing of thefirst CPMG echo train. Different sensitive volumes are measured bytransmitting each additional CPMG sequence at a different radiofrequency. In the preferred embodiment, the additional echo trains havea duration and inter echo spacing adapted to determine the presence ofcomponents in the formation having a transverse relaxation time lessthan about 33 milliseconds. The total duration of all the additionalecho trains is about equal to the duration of the first echo train. Inthe preferred embodiment, the total radio frequency power transmitted inthe all the additional echo trains is approximately equal to the radiofrequency power transmitted in the first echo train.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021]FIG. 1 shows a graph of amplitude of the static magnetic field ofthe magnet in an NMR well logging apparatus used with the invention.

[0022]FIG. 2 shows a timing diagram for radio frequency power pulsesgenerated by the NMR well logging apparatus in the method of theinvention used to measure the transverse relaxation time of earthformations.

[0023]FIG. 3 shows a timing diagram for radio frequency power pulsesused to measure longitudinal relaxation time of the earth formations.

[0024] FIGS. 4-6 show example distributions of transverse relaxationtime used to test the method of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0025] An NMR well logging apparatus which is suitable for use with thisinvention is described, for example, in U.S. patent application Ser. No.08/606,089 filed on Feb. 23, 1996 entitled “NMR Apparatus and Method”.The apparatus described in the Ser. No. 08/606,089 patent applicationincludes a magnet for inducing a static magnetic field in the earthformations. The static magnetic field includes an amplitude gradientdirected radially inwardly towards the longitudinal axis of theinstrument. The apparatus disclosed in the Ser. No. 08/606,089application includes an antenna through which pulses of RF power areconducted to excite nuclei of the earth formations surrounding theinstrument. The antenna includes a wire coil wound around a highmagnetic permeability ferrite. The ferrite includes a frequency controlcoil wound thereon. By passing a selectively controllable DC voltagethrough the frequency control coil, the tuning frequency of the antennacan be selectively controlled, making transmission and reception of RFenergy at. The apparatus disclosed in the Ser. No. 08/606,089 patentapplication can make NMR measurements at a plurality of differentfrequencies. Since the static magnetic field imparted by the magnetdisclosed in the Ser. No. 08/606,089 patent application includes anamplitude gradient, conducting NMR measurements at different frequencieswill result in these different frequency NMR measurements taking placein different sensitive (excitation) volumes.

[0026] It is to be clearly understood that the apparatus disclosed inthe Ser. No. 08/606,089 patent application is not the only apparatuswhich can be used for this invention. For purposes of this invention itis only necessary that the NMR apparatus be able to selectively excitedifferent sensitive volumes to nuclear magnetic resonance, andselectively receive NMR signals from each of the selectively excitedsensitive volumes. Using multiple frequencies for individual NMRmeasurement sequences in a gradient static magnetic field is aparticularly convenient means by which to carry out the method of thisinvention, and so the apparatus disclosed in the Ser. No. 08/606,089patent application is a particularly convenient instrument, but not theexclusive instrument by which to carry out the method of this invention.

[0027]FIG. 1 shows a graph of the amplitude of the static magneticfield, with respect to distance from the magnet, for the well loggingapparatus described in the Ser. No. 08/606,089 patent application. Theamplitude of the static magnetic field generally decreases with respectto the lateral distance from the magnet. As is well known in the art,nuclear magnetic resonance conditions occur when a radio frequencymagnetic field is applied to materials polarized along a static magneticfield where the frequency of the RF magnetic field matches the productof the static magnetic field strength and the gyromagnetic ratio of thenuclei being polarized by the static magnetic field, this product beingreferred to as the Larmor frequency. As can be inferred from the graphin FIG. 1, by adjusting the frequency of the RF magnetic field, thedistance from the magnet at which nuclear magnetic resonance conditionsoccur can be changed corresponding to the static magnetic fieldamplitude at that particular distance from the magnet. For example, iffrequency f₁ is the highest frequency, resonance will occur at thesmallest distance to the magnet, and so on through lower frequencies f₂through f_(N). Because nuclear magnetic resonance only occurs where thestatic magnetic field strength matches the RF magnetic field frequency,nuclear magnetic resonance measurements can be conducted within a numberof different non-overlapping sensitive volumes by inducing nuclearmagnetic resonance at different frequencies. A particular set ofnon-overlapping sensitive volumes which would result when using theapparatus described in the Ser. No. 08/606,089 patent application, forexample, would comprise thin annular cylinders each having an averageradius corresponding to the particular static magnetic field amplitudein which nuclear magnetic resonance would occur at a particular RFmagnetic field frequency. The thickness of each annular cylinder wouldbe related to the bandwidth of a receiver circuit in the NMR instrumentand the rate at which the static magnetic field changes in amplitude.

[0028] This feature of the static magnetic field, and the selectablefrequency capability for the RF magnetic field in the apparatusdescribed in the Ser. No. 08/606,089 patent application makes itpossible to conduct time-overlapping NMR measurements within differentsensitive volumes. By time-overlapping NMR experiments in differentsensitive volumes, it is possible to more efficiently use the RFtransmitting components in the apparatus. The manner in which the RFtransmitting components are used more efficiently will now be explained.

[0029] 1. A Multiple Frequency CPMG Pulse Sequence for Improved SNR inTransverse Relaxation Time Measurement

[0030] Nuclear magnetic transverse relaxation properties of materialsare typically measured using Carr-Purcell-Meiboom-Gill (“CPMG”) pulsesequences. For NMR relaxometry of fluids in the pore spaces of a porousmedium, the CPMG sequences should include a sufficient number of 180°rephasing pulses to acquire substantially the entire relaxationspectrum. This means that the CPMG pulse sequence should usually extendabout to the five times longest expected transverse relaxation time. Thetransverse relaxation spectrum is typically sampled at the maximumpossible pulsing rate in order not to lose any pulse echoes whoseamplitudes are related to fast relaxing (short T₂) components in theporous medium. The maximum rate corresponds to the minimum, or shortest,interecho time (TE) value of which the particular NMR instrument iscapable. However, the data acquired using the shortest TE may beredundant for acquiring information related to the slower relaxingcomponents of earth formations. It is known in the art to use thisredundancy for SNR improvement by summing the measured spin-echoamplitudes over a number of predetermined time intervals or by usingsingular value decomposition (“SVD”) analysis.

[0031] The method of applying RF pulses according to this invention canbe better understood by comparing the following two NMR pulsingsequences, which have approximately equal average power consumption. Thefirst such pulsing sequence is a polarity-alternated CPMG pulse sequencepair (referred to as a pease alternate pair sequence (“PAPS”)). PAPSsequences are known in the art and can be described by the followingexpression:

90°_(±x)−τ−(180°_(y)−2τ)_(I)−T_(r)

[0032] where I represents the number of 180° rephasing pulses (equal tothe number of echoes in the CPMG echo train), T_(r) represents the wait(repolarizing) time, and τ represents the Carr-Purcell spacing, which isequal to about ½ TE.

[0033] The NMR measurement sequence of this invention, however, isoptimized by individually exciting nuclear magnetic resonance within aquantity, J+1, of different sensitive volumes during one completemeasurement cycle. This measurement sequence is performed according asfollows. Referring now to FIG. 2, an initial PAPS measurement sequencecan be used to excite nuclei within a first sensitive volume using aCarr-Purcell spacing represented by τ′ and a number of 180° rephasingpulses represented by I′, as in the following expression:

90°_(±x)−τ′−(180°−2τ′)_(I′)−T_(r)

[0034] For clarity of the illustration in FIG. 2, only the first half ofeach PAPS sequence is shown in FIG. 2. The initial sequence is shown inFIG. 2 by a 90° pulse at frequency f₁ followed by a waiting period equalto τ′. After the waiting period, a series, numbering I′, of 180°rephasing pulses at frequency f₁, each separated by waiting period 2τ′,is applied to the antenna. (Not shown in the timing diagram of FIG. 2 isthe inverse phase measurement set corresponding to the measurement setjust described forming the second half of the PAPS measurementsequence.) The initial PAPS measurement sequence is intended to measurethe relaxation characteristics of the components of the earth formationswhich have relatively long transverse relaxation times. In the initialPAPS measurement sequence, the TE can be relatively long (for example2-4 msec, with an upper limit related to the magnitude of any gradientin the static magnetic field to avoid diffusion-related effects on theNMR signals) to minimize the total number of pulses generated, therebyminimizing the amount of power consumed in generating the pulses in theinitial PAPS measurement sequence.

[0035] The initial PAPS measurement sequence can then be followed by aseries of additional PAPS measurement sequences. These additional PAPSmeasurement sequences are used to excite nuclear magnetic resonancewithin a number, J, of additional sensitive volumes according to thefollowing expression:

(90°_(±x)−τ−(180°−2τ)_(I″)−T_(r))_(j); j=1, 2, 3, . . . , J

[0036] where I′=Iτ/τ′, J≈(I−I′)/I″, and I″ is selected to minimize therelative error for calculating the petrophysical parameters. To excitethe J+1 sensitive volumes using the NMR well logging apparatus describedin U.S. patent application Ser. No. 08/606,089, for example, a set ofJ+1 individual operating frequencies can be used, each of whichcorresponds to one of J+1 static magnetic field amplitudes locatedwithin in J+1 different spatial volumes within the earth formation.

[0037] The timing of the additional pulse sequences is shown in thelower portion of the timing diagram in FIG. 2. A 90° pulse at frequencyf₂ is transmitted. After a waiting time τ″, a shortened set, numberingI″, of 180° rephasing pulses is applied at this same frequency f₂. Thisprocedure can be repeated, almost immediately after the end of the pulsesequence transmitted at frequency f₂, by another additional pulsesequence transmitted at frequency f₃, and so on through a finaladditional pulse sequence transmitted at frequency f_(J−1). Note thatthe total number of RF pulses for all of the J additional pulsesequences can be about equal to the amount of time used in the initialPAPS sequence.

[0038] The additional pulse sequences are intended to measure relaxationcharacteristics of components of the earth formations which haverelatively short relaxation times (previously described as being lessthan about 33 msec). The TE of the additional PAPS pulse sequences istypically shorter than that of the initial PAPS sequence. Typically theTE of the additional pulse sequences should be about 0.5 msec or less,and it is contemplated that the TE can be as small as the particularwell logging apparatus is capable of using (which for at least oneinstrument known in the art is about 0.2 msec). Because the componentsof the earth formation measured using the additional pulse sequenceshave short relaxation times, the pulse sequence duration, andcorrespondingly the total number of pulses in each additional sequence,can be much smaller than it is in the initial PAPS sequence. It isexpected that since the T₂ of the formation components measured duringthe additional pulse sequences is typically less than about 33 msec, atotal sequence length of about 50 msec for each of the additional pulsesequences will be sufficient to measure the short relaxation timeformation components accurately. It should be noted, however, that thewait (recovery) time between individual measurement sequences, withineach sensitive volume, is not substantially changed because only one NMRexcitation pulse sequence occurs within each sensitive volume duringeach complete measurement cycle, because a complete measurement cycleincludes one of the initial PAPS sequences and J additional pulsesequences.

[0039] The pulse sequence of the invention was compared with prior artpulse sequences to determine the amount of improvement in the accuracyof calculated petrophysical parameters for a particular amount of RFpower in each type of pulse sequence, and for any particular amount ofnoise in the spin echo amplitude signals.

[0040] The first step in comparing the invention with prior art pulsingsequences is to generate a relaxation time distribution (also known as aspin echo amplitude decay curve) from sample T₂ distributions typical ofearth formations. Typical T₂ relaxation distributions for earthformations extend from about 1 msec to about 200 msec and are bimodal incharacter. FIGS. 4 through 6 represent typical bimodal relaxation timedistributions, denoted in several tables below as sample #1, sample #2and sample #3, respectively. The example distribution of FIG. 4 includesa relatively large amount of “free” water and a relatively small amountof “bound” water. The distribution of FIG. 5 includes a more balancedmix of free and bound water, and the distribution of FIG. 6 includes arelatively large amount of bound water. As is known in the art, thebimodal distribution of the relaxation distribution of typical earthformations is related to the presence and relative fractional amounts of“free” water and “bound” water in the earth formations. The T₂distributions shown in FIGS. 4-6 were used to generate correspondingrelaxation time distributions (spin echo amplitude curves) by simplearithmetic calculation. The relaxation time distributions thus generatedrepresent “noise free” spin echo amplitude signals, since they werecalculated explicitly from known T₂ distributions.

[0041] The next step in comparing the invention to the prior art is togenerate simulated “real” spin echo amplitude signals by stochasticsimulation, or Monte Carlo modeling of noise. The “real” amplitude decaycurve represents spin echo amplitude signals that would likely bemeasured by an actual NMR well logging instrument disposed in a mediumhaving a T₂ distribution equal to the one used to generate thecorresponding “noise free” spin echo amplitude decay curve. Thesimulated noise can be added to the “noise free” spin echo amplitudesignals to generate synthetic pulse echo amplitude signals. The amountof noise added to the “noise free” amplitude signals can be selected bythe system designer, and for convenience is described in the tablesbelow according to the apparent signal to noise ratio (“SNR”).

[0042] A set of synthetic “real” spin echo amplitude signals can begenerated to correspond to each pulse sequence method to be compared,both prior art and by the method of this invention. Then the synthetic“real” spin echo amplitude signals can be analyzed according to wellknown multi-exponential techniques based on singular value decompositionand non-negative linear least squares to determine the apparent T₂distribution of the “real” signals thus analyzed. The analysistechniques known in the art include determination of petrophysicalparameters such as apparent porosity, which can be obtained byextrapolating the spin echo amplitude to a value which would obtain at atime to first echo of zero.

[0043] A plurality of different simulated “real” spin echo amplitudesets (each one having a different simulated “noise” set added to thenoise-free spin echo amplitude set) were analyzed for each one of the T₂distributions shown in FIGS. 4-6. The apparent porosity valuescalculated from each “real” spin echo amplitude set were statisticallyanalyzed in terms of mean apparent porosity value and standard deviationof the apparent porosity value.

[0044] Below arc tables comparing the results obtained using pulsesequences of the prior art to the pulse sequence of this invention. Forthe pulsing sequences according to the prior art the followingparameters were chosen: TE=2τ=1 msec; I=1000. For the pulse sequence ofthe invention the following parameters were used: TE′=2τ′=2 msec;I′=500; TE=1 msec; I″=40; and J=12. Table 1 shows the comparativeresults for the T₂ distribution shown in FIG. 4, Table 2 shows thecomparative results for the T₂ distribution shown in FIG. 5, and Table 3shows the comparative results for the T₂ distribution shown in FIG. 6.The comparative results shown in each table represent a ratio of thestandard deviation of the calculated porosity values with respect to theaverage value of porosity and represent the ratio of the standarddeviation of the logarithmic mean of the T₂ distribution (represented byT_(2LM)) with respect to the average value of the logarithmic mean ofthe distribution. As is known in the art, higher accuracy of the resultwould correspond to a lower ratio. TABLE 1 Prior Art Multiple-FrequencyPulse Sequence Pulse Sequence σ(T_(2LM))/ σ(T_(2LM))/ SNRσ(φ_(nmr))/<φ_(nmr)> <T_(2LM)> σ(φ_(nmr))/<φ_(nmr)> <T_(2LM)> 10 0.0900.255 0.044 0.146 20 0.056 0.165 0.024 0.072 50 0.024 0.081 0.013 0.043

[0045] TABLE 2 Multiple-Frequency Prior Art Pulse Sequence PulseSequence σ(T_(2LM))/ σ(T_(2LM))/ SNR σ(φ_(nmr))/<φ_(nmr)> <T_(2LM)>σ(φ_(nmr))/<φ_(nmr)> <T_(2LM)> 10 0.082 0.241 0.047 0.137 20 0.054 0.1530.024 0.066 50 0.029 0.077 0.014 0.04

[0046] TABLE 3 Prior Art Multiple-Frequency Pulse Sequence PulseSequence σ(T_(2LM))/ SNR σ(φ_(nmr))/<φ_(nmr)> <T_(2LM)>σ(φ_(nmr))/<φ_(nmr)> <T_(2LM)σ(T_(2LM))/ 10 0.092 0.206 0.079 0.172 200.063 0.146 0.029 0.074 50 0.029 0.072 0.015 0.039

[0047] The SNR (signal to noise ratio) is defined as: [totalamplitude/standard deviation of the noise].

[0048] Improvements in the calculation of the apparent permeabilityusing the pulse sequence method of the invention can also be obtained.For example, a method of calculating permeability from NMR data calledthe “SDR” method defines permeability in terms of NMR porosity andT_(2LM) by the following relationship:

K _(nmr)∝φ_(nmr) ⁴ T _(2LM) ²

[0049] See for example, C. E. Morriss et al, Operating Guide for theCombinable Magnetic Resonance Tool, The Log Analyst, November-December1996, Society of Professional Well Log Analysts, Houston, Tex. Therelative error of permeability can be defined by the expression:

σ(K _(nmr))/<K _(nmr)>=4σ(φ_(nmr))/<φ_(nmr)>+2σ(T _(2LM))/<T _(2LM)>

[0050] A comparison table for K_(nmr) is shown below: TABLE 4 Prior ArtMultiple Frequency Pulse Sequence Pulse Sequence SNRσ(K_(nmr))/<K_(nmr)> σ(K_(nmr))/<K_(nmr)> 10 0.810 0.462 20 0.522 0.22850 0.276 0.150

[0051] Also presented below in Table 5 is a comparison with respect toprior art techniques of the relative permeability error for differentpulsing techniques according to the method of this invention each havingapproximately the same total RF energy content. The parameters for eachpulse sequence (numbered 1 through 5 below) are as follows: 1) TE′ = 2τ′= 2ms; I′ = 500 TE = 1ms I″ = 20 J = 24 SNR = 20 2) TE′ = 2τ′ = 2ms; I′= 500 TE = 1ms I″ = 40 J = 12 SNR = 20 3) TE′ = 2τ′ = 2ms; I′ = 500 TE =1ms I″ = 80 J = 6 SNR = 20 4) TE′ = 2τ′ = 2ms; I′ = 500 TE = 1ms I″ = J= 4 SNR = 20   120 5) Prior Art CPMG: I = TE = 1ms SNR = 20   1000

[0052] TABLE 5 Pulse sequence: 1 2 3 4 5 (prior art) Sample #1σ(K_(nmr))/<K_(nmr)> 0.23 0.21 0.29 0.35 0.52 Sample #2σ(K_(nmr))/<K_(nmr)> 0.24 0.24 0.23 0.31 0.55 Sample #3σ(K_(nmr))/<K_(nmr)> 0.28 0.26 0.26 0.36 0.54

[0053] It can be concluded from the results shown in Table 5 thatσ(K_(nmr))/<K_(nmr)> is substantially insensitive to the value of I″within a range of about 20-80 and, correspondingly, J being within arange of about 24-6. The expected accuracy using the pulse sequence ofthe invention is about twice that using the pulse sequences known in theart where both types of pulse sequence have about the same total RFenergy.

[0054] 2. T₁ Measurement Using Multiple Frequency Pulsing

[0055] Pulse-echo techniques known in the art for measuring NMRlongitudinal relaxation time (T₁) include inversion recovery (“IR”) andsaturation recovery (“SR”). In the IR technique, after polarization ofthe nuclei along the static magnetic field, a 180° RF pulse is appliedto the instrument's antenna, causing inversion of the nuclear spinsystem within the sensitive volume. The 180° pulse is followed by arecovery time R_(i), which is typically some predetermined value withinthe range of 0.05 to 5 times the expected value of T₁. Then a 90°“read-out” pulse is applied to the antenna. The amplitude of the freeinduction decay (“FID”) following the 90° read-out pulse is measured.This amplitude measurement forms one point on a T₁ relaxation “curve”.The relaxation curve represents a relationship of the FID amplitude withrespect to the recovery time R_(i). Typically the relaxation curve isdetermined by measuring FID amplitudes at a number of differentpredetermined recovery times. The relaxation curve can be used todetermine the relaxation time T₁, as is known in the art.

[0056] After the first read-out pulse and measurement of the FIDamplitude, the nuclear spin system is then allowed to return toequilibrium (alignment with the static magnetic field) by waiting for atime period, W. W is approximately equal to 5 times T₁. Then anotherpoint of the T₁ relaxation curve can be measured by again applying a180° pulse, waiting for a different recovery time R₂, applying another90° read-out pulse and measuring the FID amplitude. An expression forthe relaxation in inversion recovery type measurements is:

M(R _(i))=M ₀−2M ₀ exp(−R _(i) /T ₁); i=1, 2, . . . , N

[0057] Transmitting an IR pulse sequence to make T₁ measurements is verytime consuming, since an acquisition of just one point along the T₁relaxation curve requires a time span of about R_(i)+W>5(T₁).

[0058] The saturation recovery (“SR”) technique is much less timeconsuming. The nuclear spin system is initialized quickly using several90° pulses (called preparation pulses), to reduce the bulk magnetizationof the nuclei to zero, and then the nuclear spin system is allowed torecover for a predetermined length of time before applying a read-outpulse. Since the initial condition (zero magnetization) is provided bythe 90° pulses, no waiting time is required for reorientation with thestatic magnetic field. Thus an i-th point on the T₁ relaxation curve isacquired in a time interval of about R_(i). An expression for relaxationin SR type measurements is as follows:

M(R _(i))=M ₀[1−exp(−R _(i) /T ₁)]

[0059] Since in the IR technique the relaxation starts from bulk nuclearmagnetization equal to −M₀, the range of magnetization is 2M₀, ascompared to a range of M₀ in the case of the SR technique. IRmeasurements therefore typically result in higher signal-to-noise ratio,assuming that the T₁ relaxation curve is acquired during the same timeinterval as it is for the SR type measurement.

[0060] Both techniques can use CPMG pulse sequences as a substitute forthe 90° read-out pulses. Since T₂ information from the CPMG sequence isnot needed in order to measure T₁, only the sum of the echoes in eachCPMG sequence can be measured in order to increase the overallsignal-to-noise ratio. In any event, IR/CPMG and SR/CPMG techniques arerelatively time consuming to perform and so have not been usedextensively in well logging applications.

[0061] Using the multiple frequency measurement system described in theinvention, however, it is possible to provide a more time-efficienttechnique for measuring T₁, which can be described as follows. Referringnow to FIG. 3, a plurality of different sensitive volumes prepolarizedalong a static magnetic field are inversely polarized in rapidsuccession. The inverse polarizations are performed by transmitting, inrapid succession, a series of (“inverting”) 180° RF pulses atfrequencies each corresponding to the static magnetic field amplitude inone of the sensitive volumes. This is shown in FIG. 3 as a number, N, of180° “inversion” pulses, one pulse at each of frequencies f₁ throughf_(N). There need be virtually no waiting time between inversepolarization pulses for each one of the individual sensitive volumesbecause there is substantially no nuclear magnetic interaction betweenthe sensitive volumes. The minimum time delay between each inversepolarization pulse is practically limited, therefore, only by the rateat which the NMR logging instrument can transmit 180° pulses atdifferent frequencies.

[0062] The 180° inversion pulses can then be followed by a first(shortest) recovery time R₁, after which a first “read-out” CPMG pulsesequence is transmitted, shown in FIG. 3 at CPMG@f₁, which has aduration T_(tr). The first CPMG sequence is transmitted at the firstfrequency, which can be the same frequency as the first 180° inversionpulse. The amplitudes of the echoes in the first CPMG sequence aremeasured to determine the first “point” of the T₁ relaxation curve.

[0063] A second CPMG sequence can then be transmitted at the secondfrequency (shown at CPMG@f₂) after a second recovery time R₂>R₁+T_(tr).A second “point” on T₁ relaxation curve is then acquired form the echoamplitude measurements of the second CPMG sequence, starting at t=R₂.After a third recovery time R₃>R₂+T_(tr), a third CPMG sequence (shownat CPMG@f₃) can be transmitted at the third frequency. The third “point”on the T₁ relaxation curve can be acquired by measurement of the echoamplitudes in the third CPMG sequence.

[0064] The transmission of CPMG sequences can then be repeated, at eachremaining frequency, for as many as the number of frequencies, N,originally transmitted as 180° inversion pulses. There will then be Npoints on the relaxation curve measured from N different excitationvolumes. To acquire a complete T₁ relaxation curve, the last recoverytime R_(N) is preferably equal to approximately the waiting time W (aspreviously explained, about equal to 5 times T₁). The T₁ measurementsequence performed according to this method may be run substantiallycontinuously, as suggested by the timing diagram of FIG. 3, since thefirst sensitive volume will have substantially reestablished its initialmagnetization M₀ by the time of completion of measurement of the last(N-th) point of the T₁ curve. It is contemplated that about thirtyfrequencies (N=30) will provide sufficient sampling to accuratelydetermine the T₁ relaxation curve.

[0065] Below is a comparison of the duration of T₁ relaxation curveacquisition experiments for using SR/CPMG of the prior art and themethod of this invention. Considering logarithmic spaced points,advantageous:

R _(i) =R ₁2^(i)

[0066] Then an SR/CPMG sequence requires approximately (time requiredfor each CPMG sequence is assumed to negligible):$T_{SR} = {{\sum\limits_{i = 1}^{N}{R_{1}2^{i}}} = {R_{1}\left( {2^{N + 1} - 1} \right)}}$

[0067] For the T₁ measurement pulse sequence of the invention, thesequence has N−1 measurement enclosed in the last and the longest R_(N)interval, therefore:

T=R _(N) =R ₁2^(N).

[0068] Note that an IR measurement sequence would require a timeT_(IR)=N R₁ (2^(N+1)−1), which is about 2N times more than the timeneeded for the pulse sequence according to the invention. A comparisonof signal-to-noise ratio (SNR) between the invention and SR sequencesper unit time can be expressed as:

SNR/SNR_(SR)=2(T _(SR) /T)^(½)≈2.8

[0069] The factor 2 appearing in the last equation is due to themagnetization range 2M₀ in the sequence of the invention as opposed tothe magnetization range M₀ for the SR/CPMG sequence known in the art.

[0070] It should be noted that the method for measuring T₁ disclosedherein is not limited to well logging applications. For example, T₁measurement of core samples of the earth formations removed from thewellbore can be made much more efficient using the method of thisinvention. Other applications for T₁ can be similarly improved using themethod of this invention.

[0071] Those skilled in the art will devise other embodiments of thisinvention which do not depart from the spirit of the invention disclosedherein. Accordingly, the scope of the invention should be limited onlyby the attached claims.

What is claimed is:
 1. A method for determining nuclear magneticresonance longitudinal relaxation time of a medium, comprising:magnetically polarizing nuclei in said medium along a static magneticfield; momentarily inverting said magnetic polarization of said nucleiwithin each one of a plurality of different spatial volumes within saidmedium; transversely magnetizing said nuclei in each one of said spatialvolumes after a different recovery time for each one of said spatialvolumes; and measuring a magnetic resonance signal from each one of saidspatial volumes.
 2. The method as defined in claim 1 wherein said staticmagnetic field comprises a different amplitude within each one of saidspatial volumes.
 3. The method as defined in claim 2 wherein said stepof inversely polarizing comprises transmitting 180 degree radiofrequency pulses at a frequencies corresponding to the amplitude of saidstatic magnetic field within each one of said spatial volumes.
 4. Themethod as defined in claim 1 wherein said steps of transversemagnetizing and measuring said signal comprises CPMG pulse sequences. 5.A method of nuclear magnetic resonance measurement of a medium,comprising: magnetically polarizing nuclei in said medium with a staticmagnetic field; acquiring a first CPMG echo train in a first sensitivevolume having a duration large enough to determine presence of slowlyrelaxing components in said medium; acquiring a plurality of additionalCPMG echo trains, each of said additional echo trains corresponding to adifferent sensitive volume, each of said additional CPMG echo trainshaving a duration less than said duration and echo spacing of said firstCPMG echo train.
 6. The method as defined in claim 5 wherein said firstand said additional CPMG echo trains are acquired using a differentradio frequency for each of said echo trains, whereby each of said echotrains corresponds to a different sensitive volume in said medium. 7.The method as defined in claim 5 wherein said interecho spacing and saidduration of said first echo train are adapted to determined presence ofcomponents in said medium having a transverse relaxation time greaterthan about 33 milliseconds.
 8. The method as defined in claim 5 whereinsaid interecho spacing and said duration of said additional echo trainsare adapted to determined presence of components in said medium having atransverse relaxation time less than about 33 milliseconds.
 9. Themethod as defined in claim 5 wherein an average radio frequency powertransmitted in acquiring said first echo train is approximately equal toan average radio frequency power transmitted in acquiring all of saidadditional echo trains.
 10. The method as defined in claim 5 whereinsaid duration of said first echo train is approximately equal to the sumof the durations of all of said additional echo trains.